Skip Navigation

Biometrika 1987 74(3):563-570; doi:10.1093/biomet/74.3.563
© 1987 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by HAITOVSKY, Y.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

On multivariate ridge regression

YOEL HAITOVSKY

Departments of Statistics and Economics, Hebrew University of Jerusalem Jerusalem 91905, Israel

A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p × q parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the ‘across regression’ correlations, and ignores the Stein effect. A remedy was offered by Brown & Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting the model in a linear hierarchical framework, obtaining the Brown & Zidek multivariate ridge estimates, Efron & Morris's estimates of several normal mean vectors and Fearn's Bayesian estimates of growth curves as special cases. The unknown covariance case results in an identifiability problem, which can be overcome by a Bayesian approach using conjugate priors for the unidentified covariance matrices.

Key Words: Bayes estimates • EM algorithm • Exchangeability • Lindley-Smith modal estimate • Linear hierarchical model • Maximum likelihood • Mean of multivariate normal distribution • Multivariate regression • Ridge regression • Stein estimator


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.